That unit is still considered a general. You can verify that in battle..when it says "The Enemy General Flees" Instead of "The Enemy King Flees".

Also you can play as the rebels if you want. Then you see that they are all the same Faction..technicaly.

Even more in depth. The factions are declared in the Starpos file. Khazar is listed, but as rebel.

When you conquer that province..and get it to rebel after several turns. You can spawn 2 rebel armies in the same province...one is Khazars and other is Rebels. But they both fight together as allies in the battle. And this doesn't always happen, it just depends on how your loyalty is upgraded.